A review and comparison of solvers for convex MINLP

Abstract

In this paper, we present a review of deterministic software for solving convex MINLP problems as well as a comprehensive comparison of a large selection of commonly available solvers. As a test set, we have used all MINLP instances classified as convex in the problem library MINLPLib, resulting in a test set of 335 convex MINLP instances. A summary of the most common methods for solving convex MINLP problems is given to better highlight the differences between the solvers. To show how the solvers perform on problems with different properties, we have divided the test set into subsets based on the continuous relaxation gap, the degree of nonlinearity, and the relative number of discrete variables. The results also provide guidelines on how well suited a specific solver or method is for particular types of MINLP problems.